Find the principal and general solutions of the following equations:

Q (4)  \small cosec x = -2

Answers (1)

We know that
                    cosec \frac{\pi}{6} = 2
                  
                   cosec (\pi + \frac{\pi}{6}) = -cosec\frac{\pi}{6} = -2               and also                cosec (2\pi - \frac{\pi}{6}) = cosec\frac{11\pi}{6} = -2
So,
                   cosec x= cosec\frac{7\pi}{6}                                  and                                   cosec x= cosec\frac{11\pi}{6}

So, the principal solutions are x = \frac{7\pi}{6} \ and \ \frac{11\pi}{6} 
 

 

Now,
             cosec x= cosec\frac{7\pi}{6}
             
              \sin x = \sin\frac{7\pi}{6}                                                                                     \left ( \because \sin x = \frac{1}{cosec x} \right )

          x = n\pi + (-1)^{n}\frac{7\pi}{6}
Therefore, the general solution is

  x = n\pi + (-1)^{n}\frac{7\pi}{6}     

where n \ \epsilon \ Z

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout NEET May 2022

An exhaustive E-learning program for the complete preparation of NEET..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions